Position Sizing: Alternatives to the Kelly Criterion

Deciding how much to invest in a given position is often a more decisive factor for long-term performance than the buy or sell signal itself. This discipline, known as position sizing, directly determines a portfolio's survival through the inevitable losing streaks that occur in financial markets.

While the Kelly criterion is often cited as the theoretical benchmark for maximizing a capital's geometric growth, most investors and traders rely in practice on simpler, more robust methods. This article explores these alternatives, their respective trade-offs, and why a middle-ground approach often emerges as the most sensible choice.

A brief reminder on the Kelly criterion

The Kelly criterion mathematically computes the optimal fraction of capital to commit to a given bet, based on the probability of winning and the expected win/loss ratio, in order to maximize the capital's long-term geometric growth. Its exact formula and subtleties have already been covered in detail in another article on the site; we won't repeat them here. What matters here is simply that full Kelly is notoriously aggressive and highly sensitive to probability estimation errors, which pushes most practitioners toward alternative methods or toward reduced Kelly fractions.

Fixed-dollar sizing

The simplest method consists of investing a fixed amount, say €500, in every position, regardless of the portfolio's size at the time the position is opened or the intrinsic risk level of the asset in question.

Advantages and limits

Its simplicity is its main strength: no complex calculation is required, making it accessible to beginners. Its major limitation is that it completely ignores each position's relative risk: an asset twice as volatile as another receives exactly the same capital allocation, which unbalances each position's contribution to the portfolio's total risk.

Fixed fractional sizing

This method allocates a constant percentage of total capital to each position, for example 2% of available capital. Unlike fixed-dollar sizing, position size automatically scales with the growth or decline of total capital, introducing a compounding effect on both gains and losses.

The 2% rule

Very popular in retail trading risk management, the 2% rule states that no single position should expose the portfolio to a loss greater than 2% of total capital in an adverse scenario — that is, if the stop-loss is hit. The amount invested in the position is therefore calculated from the distance between the entry price and the stop-loss level, rather than from a raw percentage of capital allocated to the purchase.

Why this refinement changes everything

This nuance is essential: the 2% rule doesn't specify how much capital to buy, but how much capital to risk. Two assets with very different volatilities will therefore receive different position sizes for the same maximum loss risk, which already brings this method closer to a risk-adjustment logic, without explicitly using a statistical volatility measure.

Volatility-based sizing

The principle

This more sophisticated method sizes each position inversely proportional to its recent volatility, measured for example by ATR (Average True Range) or by the standard deviation of realized returns. The goal is for each position to contribute roughly the same level of risk to the overall portfolio, regardless of the nature of the underlying asset.

A calculation example

If asset A has a daily ATR of €2 and asset B has an ATR of €8, volatility-based sizing will allocate roughly four times as many units of asset A as of asset B for the same currency risk budget, since each unit of B is four times as volatile as a unit of A.

Why this method is considered more robust

By equalizing each position's contribution to risk, volatility-based sizing prevents a single highly volatile asset from disproportionately dominating the portfolio's total risk — a frequent problem with fixed-dollar sizing and, to a lesser extent, with fixed fractional sizing applied without adjusting for each asset's intrinsic risk.

Worked example: one signal, three different sizes

Suppose a €50,000 portfolio and a buy signal on a stock trading at €100, with a stop-loss set at €92 (an €8 risk per share) and a daily ATR of €3.

Fixed-dollar method

With a fixed allocation of €5,000 per position, the investor buys 50 shares, without regard to the risk level associated with this specific position relative to the portfolio's other positions.

The 2% rule method

With total capital of €50,000, the maximum tolerated risk is €1,000 (2% of €50,000). With an €8 risk per share, the investor can buy 125 shares, a capital commitment of €12,500 — far more than the fixed method, because the stop-loss sits relatively close to the entry price.

Volatility-based method

Targeting, for example, a risk budget of €300 per day of normal volatility (as measured by ATR), and with an ATR of €3 per share, the investor buys 100 shares, a capital commitment of €10,000. This result sits between the two previous methods, reflecting consideration of both stop-loss risk and the asset's normal daily volatility.

These three very different outcomes for the same entry signal illustrate how much the choice of sizing method can affect a portfolio's actual exposure, well before even considering the question of entry or exit timing.

Comparing simplicity and risk-adjustment quality

Fixed-dollar sizing is the simplest method but the least suited to each position's actual risk. The 2% rule introduces a notion of risk via the stop-loss, a substantial improvement, but it ignores the asset's normal volatility outside the stop-loss scenario. Volatility-based sizing offers the most complete risk adjustment, at the cost of greater calculation complexity and the need for reliable, up-to-date volatility data.

Why volatility-based sizing is often the more robust middle ground

Full Kelly, while theoretically optimal for maximizing a capital's geometric growth, is extremely sensitive to errors in estimating win probability and the win/loss ratio — parameters that are nearly impossible to know with certainty in real financial markets. Even a modest estimation error can lead full Kelly to recommend dangerously excessive position sizes.

Volatility-based sizing, by contrast, relies only on an observable, relatively stable statistical measure over time — the asset's recent volatility — without requiring any estimate of win probabilities. It thus occupies a sensible middle ground between the somewhat crude simplicity of fixed-dollar sizing and the potentially dangerous aggressiveness of full Kelly, which explains its growing popularity among professional risk managers.

Summary and next steps

Position sizing isn't limited to the Kelly criterion alone. Fixed methods offer simplicity but little risk adjustment, the 2% rule introduces protection against maximum tolerated losses, and volatility-based sizing pushes risk adjustment further by equalizing each position's contribution to overall portfolio risk.

To test the impact of different position sizing methods on your own investment scenarios, the simulation tools available at /outils let you explore these calculations for educational purposes, never as personalized investment advice.